Finite Group Databasebeta

← #28502928

Subgroups — #28502928

Order 15104.

234 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 234 conjugacy classes of subgroups — too many to draw. Only its 55 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21426345C211yesmaximal, characteristic, complemented
2#21426173C211yesmaximal, characteristic, complemented
3#21426169C211yesmaximal, characteristic, complemented
4#21425932C211yesmaximal, characteristic, complemented
5#21422171C211yesmaximal, characteristic, complemented
6#21422132C211yesmaximal, characteristic, complemented
7C59×#1357C211yesmaximal, characteristic, complemented
8#16837840—21no—
9#16837838—21no—
10C2×#14273668—21no—
11C2×#14273668—21no—
12#16837820—21no—
13#16837779C2211yescharacteristic
14#16837520C2211yescharacteristic
15#16837223C2211yescharacteristic
16#16837216—21no—
17#16837215—21no—
18#16837187—21no—
19C4×C59⋊C16C2211yescharacteristic
20C59×#493C2211yescharacteristic
21C59×#364C2211yescharacteristic
22C59×#364C2211yescharacteristic
23#14273749D411yescharacteristic
24C2×D472—21no—
25C2×D472—21no—
26#14273733—21no—
27#14273724—21no—
28#14273672—41no—
29#14273671—41no—
30D944—41no—
31#14273668—42no—
32#14273668—41no—
33#14273668—41no—
34#14273668—41no—
35#14273667—21no—
36#14273666—41no—
37C2×C59⋊C16D411yescharacteristic
38C2×C59⋊C16D411yescharacteristic
39C16×D59—41no—
40#14273663D411yescharacteristic
41#14273655—21no—
42C2×D8×C59—21no—
43C2×D8×C59—21no—
44#127×C59—21no—
45M32×C59—21no—
46M32×C59—21no—
47C4×C8×C59C2311yescharacteristic
48C2×D4×C59—41no—
49C2×D4×C59—81no—
50#11745685—21no—
51C2×D236—41no—
52C2×D236—81no—
53D8×C59—41no—
54D8×C59—41no—
55D8×C59—41no—
56D8×C59—41no—
57C2×C8×C59C2×D411yescharacteristic
58C2×C8×C59C2×D411yescharacteristic
59C42×C59#4111yescharacteristic
60#11745664—21no—
61Dic236D811yescharacteristic
62D472—41no—
63D472—41no—
64D472—41no—
65D472—41no—
66D472D811yescharacteristic
67#11745660—21no—
68#11745659—41no—
69C8×D59—41no—
70C16×C59—41no—
71C16×C59—41no—
72C59⋊C16—21no—
73C59⋊C16—41no—
74C59⋊C16D811yescharacteristic
75C59⋊C16D811yescharacteristic
76C23×C59—81no—
77C22×D59—81no—
78D4×C59—81no—
79D4×C59—81no—
80D4×C59—162no—
81C2×C4×C59—21no—
82C2×C4×C59#12111yescharacteristic
83C22⋊D59—41no—
84D236—21no—
85D236—81no—
86D236—81no—
87D236—162no—
88C4×D59—41no—
89Dic118—21no—
90C8×C59C2×D811yescharacteristic
91C8×C59C2×D811yescharacteristic
92C8×C59#13511yescharacteristic
93C8×C59AGL(1,ℤ/8)11yescharacteristic
94C59⋊C8—41no—
95#12436—591nomaximal, Sylow
96C22×C59—162no—
97C22×C59—161no—
98C22×C59#47211yescharacteristic
99C2×D59—41no—
100C2×D59—162no—
101C2×D59—161no—
102C4×C59—22no—
103C4×C59#45911yescharacteristic
104C4×C59#46611yescharacteristic
105Dic59—41no—
106#2246—591no—
107#2213—591no—
108#2213—591no—
109#2170—591no—
110#1373—591no—
111#1357—591no—
112#1357D5911yescharacteristic, complemented
113C2×C59—21no—
114C2×C59—321no—
115C2×C59#166711yescharacteristic
116D59—81no—
117D59—321no—
118#509—1181no—
119#509—1181no—
120C2×D16—1181no—
121C2×D16—1181no—
122#504—1181no—
123#493—591no—
124#493C2×D5911yescharacteristic
125#443—591no—
126#364—591no—
127#364C2×D5911yescharacteristic
128#364C2×D5911yescharacteristic
129#361—1181no—
130#361—1181no—
131#350—1181no—
132C4×C16—591no—
133C59#1243611yescharacteristic, complemented, Sylow
134#135—591no—
135C2×D8—21no—
136C2×D8—21no—
137C2×D8—1181no—
138C2×D8—1181no—
139#131—1181no—
140#127—21no—
141#127—1181no—
142SD32—2361no—
143SD32—2361no—
144D16—2361no—
145D16—2361no—
146D16—2361no—
147D16—2362no—
148D16—2361no—
149M32—21no—
150M32—21no—
151M32—1181no—
152M32—2361no—
153C2×C16—591no—
154C2×C16—591no—
155C2×C16—2361no—
156#108—591no—
157#104—1181no—
158C4×C8C22×D5911yescharacteristic
159#41—1181no—
160C2×D4—41no—
161C2×D4—81no—
162C2×D4—4721no—
163C2×D4—2361no—
164Q16—591no—
165SD16—1181no—
166D8—41no—
167D8—41no—
168D8—41no—
169D8—41no—
170D8—591no—
171D8—2361no—
172D8—2361no—
173D8—2361no—
174D8—2361no—
175M16—1181no—
176M16—2361no—
177C2×C8—2361no—
178C2×C8D4×D5911yescharacteristic
179C2×C8D4×D5911yescharacteristic
180C42#1174568511yescharacteristic
181C16—41no—
182C16—41no—
183C16—591no—
184C16—591no—
185C16—1181no—
186C16—2361no—
187C23—81no—
188C23—4721no—
189Q8—1181no—
190D4—81no—
191D4—81no—
192D4—162no—
193D4—1181no—
194D4—9442no—
195D4—4721no—
196D4—4721no—
197D4—2361no—
198C2×C4—21no—
199C2×C4—2361no—
200C2×C4#1427370011yescharacteristic
201C8—2361no—
202C8D8×D5911yescharacteristic
203C8D8×D5911yescharacteristic
204C8#1427374811yescharacteristic
205C8#1427375411yescharacteristic
206C22—162no—
207C22—161no—
208C22—9442no—
209C22—9441no—
210C22—2361no—
211C22#1683767111yescharacteristic
212C4—22no—
213C4—2361no—
214C4#1683759611yescharacteristic
215C4#1683763711yescharacteristic
216C2—21no—
217C2—321no—
218C2—18881no—
219C2—4721no—
220C2#2142345011yescharacteristic
subgroupG/H
centerC2#21423450
commutator, cosocleC4×C8×C59C23
FrattiniC4×C8C22×D59
FittingC59×#1357C2
socleC2×C59#1667
hypercenter#1357D59
hypocenterC59#12436
LCSG ▷ C4×C8×C59 ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C2 ◁ C2×C4 ◁ C4×C8 ◁ #1357

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #21426345C2semidirect
2. #21426173C2semidirect
3. #21426169C2semidirect
4. #21425932C2semidirect
5. #21422171C2semidirect
6. #21422132C2semidirect
7. C59×#1357C2semidirect
112. #1357D59semidirect
133. C59#12436semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#214263452
#214261732
#214261692
#214259322
#214221712
#214221322
C59×#13572
#1243659